Restricted Hidden Cardinality Constraints in Causal Models

TL;DR

This paper investigates causal models with unobserved variables of known size, deriving inequality constraints from d-separation and exploring implications for quantum systems to better understand causal influence.

Contribution

It introduces a framework for causal models with known unobserved variable cardinalities and derives related inequality constraints, extending to quantum system models.

Findings

Derived inequality constraints from d-separation in models with known unobserved cardinalities

Explored potential applications of these constraints to quantum causal models

Provided insights into causal influence in models involving quantum systems

Abstract

Causal models with unobserved variables impose nontrivial constraints on the distributions over the observed variables. When a common cause of two variables is unobserved, it is impossible to uncover the causal relation between them without making additional assumptions about the model. In this work, we consider causal models with a promise that unobserved variables have known cardinalities. We derive inequality constraints implied by d-separation in such models. Moreover, we explore the possibility of leveraging this result to study causal influence in models that involve quantum systems.